In this paper we introduce a Ramsey type function S(r; a, b, c) as the maximum s such that for any r-coloring of N there is a monochromatic sequence x1, x2, . . . , xs satisfying a homogeneous second order linear recurrence axi + bxi+1 + cxi+2 = 0, 1 6 i 6 s − 2. We investigate S(2; a, b, c) and evaluate its values for a wide class of triples (a, b, c).

We present two tools, which could be useful in determining whether or not a non-Homogenous Linear Recurrence can reach a desired rational. First, we derive the determinant that is equal to the i term in a non-Homogenous Linear Recurrence. We use this to derive the infinite determinant that is zero, if and only if, the desired rational can be reached by some term in the recurrence. Second, we de...

Motivated by the famous Skolem-Mahler-Lech theorem we initiate in this paper the study of a natural class of determinantal varieties which we call Vandermonde varieties. They are closely related to the varieties of linear recurrence relations of a given order possessing a non-trivial solution vanishing at a given set of integers. In the regular case, i.e. when the dimension of a Vandermonde var...

0 Introduction In their recent IPL paper H.N. Reddy and E.L. Leiss RL94] present an O(log N) algorithm for solving linear recurrences on hypercubic architectures. The authors go to great lengths to construct an algorithm that appears to be correct. First they construct a solution for a completely connected architecture (say a CREW PRAM) and remark that it is similar to a parallel preex computat...

When comparing a new method of measurement with a standard method, one of the things we want to know is whether the difference between the measurements by the two methods is related to the magnitude of the measurement. A plot of the difference against the standard measurement is sometimes suggested, but this will always appear to show a relation between difference and magnitude when there is no...

The plotting of cumulative sums (cusums), a technique of proven value in the detection of trends in data collected at intervals of time, may be modified to analyze circadian blood pressure patterns quantitatively. Mean 24-hour ambulatory blood pressure is taken as the reference value and is subtracted from each pressure value. The products of the remainders and the corresponding time intervals ...

Many studies have reported tree growth reduction in forests with pedestrian trampling, implying a reduction of tree transpiration in such forests. We undertook observations of tree transpiration based on the heat-pulse method in a forest (Lithocarpus edulis) with pedestrian trampling. We prepared trampled and control plots in the forest. Tree transpiration in the trampled plot was reduced compa...

spectral data from E. coli, S. aureus and P. aeruginosa infected C57BL/6 wild-type mice, showing the separation between samples along the type of infection (Fig.1A) and scores plot of the metabolite concentrations found in TLR4 deficient mice with LPS treatment and E. coli infection (Fig.1B). Two components encapsulate 82 % (A) and 90 % (B) of the interclass variation. Fig.2: The coefficient pl...